Properties

Label 8033.14
Modulus $8033$
Conductor $8033$
Order $1932$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(8033)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([897,1183]))
 
pari: [g,chi] = znchar(Mod(14,8033))
 

Basic properties

Modulus: \(8033\)
Conductor: \(8033\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(1932\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 8033.cw

\(\chi_{8033}(14,\cdot)\) \(\chi_{8033}(18,\cdot)\) \(\chi_{8033}(50,\cdot)\) \(\chi_{8033}(56,\cdot)\) \(\chi_{8033}(72,\cdot)\) \(\chi_{8033}(77,\cdot)\) \(\chi_{8033}(101,\cdot)\) \(\chi_{8033}(105,\cdot)\) \(\chi_{8033}(114,\cdot)\) \(\chi_{8033}(119,\cdot)\) \(\chi_{8033}(134,\cdot)\) \(\chi_{8033}(135,\cdot)\) \(\chi_{8033}(142,\cdot)\) \(\chi_{8033}(153,\cdot)\) \(\chi_{8033}(166,\cdot)\) \(\chi_{8033}(200,\cdot)\) \(\chi_{8033}(224,\cdot)\) \(\chi_{8033}(234,\cdot)\) \(\chi_{8033}(246,\cdot)\) \(\chi_{8033}(282,\cdot)\) \(\chi_{8033}(288,\cdot)\) \(\chi_{8033}(301,\cdot)\) \(\chi_{8033}(308,\cdot)\) \(\chi_{8033}(321,\cdot)\) \(\chi_{8033}(322,\cdot)\) \(\chi_{8033}(375,\cdot)\) \(\chi_{8033}(387,\cdot)\) \(\chi_{8033}(396,\cdot)\) \(\chi_{8033}(404,\cdot)\) \(\chi_{8033}(414,\cdot)\) ...

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Values on generators

\((5541,1944)\) → \((e\left(\frac{13}{28}\right),e\left(\frac{169}{276}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{153}{322}\right)\)\(e\left(\frac{845}{1932}\right)\)\(e\left(\frac{153}{161}\right)\)\(e\left(\frac{1597}{1932}\right)\)\(e\left(\frac{1763}{1932}\right)\)\(e\left(\frac{41}{966}\right)\)\(e\left(\frac{137}{322}\right)\)\(e\left(\frac{845}{966}\right)\)\(e\left(\frac{583}{1932}\right)\)\(e\left(\frac{863}{966}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{1932})$
Fixed field: Number field defined by a degree %d polynomial (not computed)